Difference between revisions of "1964 AHSME Problems/Problem 20"
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− | For any polynomial, even a polynomial with more than one variable, the sum of all the coefficients (including the constant, which is the coefficient of <math>x^0y^0</math>) is found by setting all variables equal to <math>1</math>. Note that we don't have to worry about whether a constant is a coefficient of an "invisible <math>x^0y^0</math> | + | For any polynomial, even a polynomial with more than one variable, the sum of all the coefficients (including the constant, which is the coefficient of <math>x^0y^0</math>) is found by setting all variables equal to <math>1</math>. Note that we don't have to worry about whether a constant is a coefficient of an "invisible" <math>x^0y^0</math> term, because there is no such term here. |
Setting <math>x=y=1</math> gives <math>(-1)^{18}</math>, which is equal to <math>1</math>, which is answer <math>\boxed{\textbf{(B)}}</math>. | Setting <math>x=y=1</math> gives <math>(-1)^{18}</math>, which is equal to <math>1</math>, which is answer <math>\boxed{\textbf{(B)}}</math>. |
Latest revision as of 22:29, 23 July 2019
Problem 20
The sum of the numerical coefficients of all the terms in the expansion of is:
Solution
For any polynomial, even a polynomial with more than one variable, the sum of all the coefficients (including the constant, which is the coefficient of ) is found by setting all variables equal to . Note that we don't have to worry about whether a constant is a coefficient of an "invisible" term, because there is no such term here.
Setting gives , which is equal to , which is answer .
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |
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